Back to Creative Math Prompts                    Previous prompt for Later Grades                   Next prompt for Later Grades
 

Thought for the day: Guide students to notice and wonder throughout the problem-solving process: (1) creating or clarifying the problem (2) exploring the question (3) reasoning about their conjectures and strategies (4) reflecting on their conclusions and thinking of new questions to ask.

Concepts: Fibonacci numbers; the golden ratio; length and area; analyzing and extending geometric, numeric, and algebraic patterns; rational and irrational numbers; similarity

Examples of noticing and wondering

I notice that the squares get larger in a counterclockwise pattern.
I notice a pattern in the side lengths of the squares.
I notice that the next square in the pattern will be on the top, and it will have 13 squares on each side.
I notice rectangles that are almost, but not quite, similar.
I notice that the ratios of the side-lengths of these rectangles alternate up and down, changing by less each time: 2, 1.5, 1.66666..., 1.6, 1.625. (These ratios are both within and between the rectangles.)

I wonder if there are patterns in the areas of the squares and rectangles.
I wonder if the ratios of the side lengths are approaching some particular number.
I wonder if the areas also have ratios that approach a particular number.
I wonder if there is a simple relationship between the eventual ratios of the side lengths and areas.
I wonder how the patterns would change if I started with three 1-by-1 squares instead of two.